please prove Q9.... 9. If α is a curve with K > 0 and τ both constant, show that α is a circular helix 9. If α is a curve with K > 0 and τ both constant, show that α is a circular helix
Prove that a unit speed curve with k and tour constant is a helix circular. unit speed 3(10pts). Prove that with is and constant curve a T circular helix. unit speed 3(10pts). Prove that with is and constant curve a T circular helix.
Consider the production function given by Q = l^α + k^α where α > 0. At what values of α does the production technology exhibit increasing, decreasing, or constant returns to scale? Prove your answer!
Help please! Let Be be Brownian motion and fix to > 0. Prove that By: = Bto+t - Blo; t o is a Brownian motion.
Let S be a finite set with cardinality n>0. a. Prove, by constructing a bijection, that the number of subsets of S of size k is equal to the number of subsets of size n- k. Be sure to prove that vour mapping is both injective and surjective. b. Prove, by constructing a bijection, that the number of odd-cardinality subsets of S is equal to the number of even-cardinality subsets of S. Be sure to prove that your mapping is...
2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a E R3 with R3 be smooth with = 1 and curvature k and torsion r, both Assume there exists a unit Ta constant = COS a. circular helix is an example of such curve a) Show that b) Show that N -a 0. c) Show that k/T =constant ttan a 2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a...
2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α 0 and for every 0 < i k one has that α, κ α, > , αϊ-1 3. Find a linear system with real coefficients for which the span of 2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α...
Here we have the production function y=f(K,L)=K3L, where K is capital input and L is labor input. Let K>0, L>0. 1. What are the marginal products of capital and labor re- spectively? 2. Please compute the technical rate of substitution (we as- sume K is on the horizontal axis). 3. Dose this production function show diminishing technical rate of substitution (in absolute value) when K increases? Please give a brief proof. 4. Please prove that this production function features increas-...
prove that J2(x)=sum from k=0 to infinity [ (-1)^k/2^9@k+2)*k!(k+2)! ]*x^(2k+2) is a solution of the Bessel differential equation of order 2: x^2y'' + xy' + (x^2-4)y=0 (-1)4 9- Using the ratio test, one can easily show that the series +2converges for all e R. Prove that (-1)X h(x) = E, 22k +2k!(k + 2)! 22+2 is a solution of the Bessel differential equation of order 2: In(x) is called the Bessel function of the first Remark. In general the function...
show work please 6. Given an indifference curve U. = 100 = F S (F>O and S>0) of the indifference a) Use the implicit function rule to derive the slope curve. b) At S = 144, Calculate the slope.